Producing melt-blown polymeric or oligomeric fibers and non-woven webs with small fiber diameters and narrow distributions of fiber diameters at commercially effective conditions is difficult. Commercial melt-blowing machines have difficulty in producing these fiber sizes at standard throughputs with conventional polymer compositions and generally can only achieve such fiber sizes at decreased throughput rates and/or extreme processing conditions if at all. In order to commercially produce fiber with diameters on the order of from less than one micron to three microns, very high Melt Flow Index (MFI) materials are required and their MFI values can exceed 2000: only a limited number of such materials are known, including for example high MFI polypropylene. Unfortunately, these high MFI materials (low molecular weight) materials inherently suffer from poor physical properties, and thus produce poor fiber and non-woven products. Other factors that can significantly increase melt-blown fiber production costs, to achieve acceptable non-woven web production rates, include: energy for high polymer melt temperatures, (often in the range of from 230° C.-350° C. or greater), high Stretch Air (SA) temperature (often as high as or higher than the melt temperature), and large Stretch Air volumes.